Pandas Profiling Report

Dataset statistics

Number of variables	20
Number of observations	4250
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	1.7 MiB
Average record size in memory	426.5 B

Variable types

NUM	15
BOOL	3
CAT	2

Reproduction

Analysis started	2021-11-04 18:40:12.041815
Analysis finished	2021-11-04 18:40:56.725805
Duration	44.68 seconds
Version	pandas-profiling v2.7.1
Command line	`pandas_profiling --config_file config.yaml [YOUR_FILE.csv]`
Download configuration	config.yaml

`state` has a high cardinality: 51 distinct values	High cardinality
`total_day_charge` is highly correlated with `total_day_minutes`	High correlation
`total_day_minutes` is highly correlated with `total_day_charge`	High correlation
`total_eve_charge` is highly correlated with `total_eve_minutes`	High correlation
`total_eve_minutes` is highly correlated with `total_eve_charge`	High correlation
`total_night_charge` is highly correlated with `total_night_minutes`	High correlation
`total_night_minutes` is highly correlated with `total_night_charge`	High correlation
`total_intl_charge` is highly correlated with `total_intl_minutes`	High correlation
`total_intl_minutes` is highly correlated with `total_intl_charge`	High correlation
`number_vmail_messages` has 3139 (73.9%) zeros	Zeros
`number_customer_service_calls` has 886 (20.8%) zeros	Zeros

state
Categorical

HIGH CARDINALITY

Distinct count	51
Unique (%)	1.2%
Missing	0
Missing (%)	0.0%
Memory size	33.3 KiB

WV	139
MN	108
ID	106
AL	101
VA	100
Other values (46)	3696

Value	Count	Frequency (%)
WV	139	3.3%
MN	108	2.5%
ID	106	2.5%
AL	101	2.4%
VA	100	2.4%
OR	99	2.3%
TX	98	2.3%
UT	97	2.3%
NY	96	2.3%
NJ	96	2.3%
Other values (41)	3210	75.5%

Length

Max length	2
Mean length	2
Min length	2

Value	Count	Frequency (%)
Uppercase_Letter	24	100.0%

Value	Count	Frequency (%)
Latin	24	100.0%

Value	Count	Frequency (%)
ASCII	24	100.0%

account_length
Real number (ℝ_≥0)

Distinct count	215
Unique (%)	5.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	100.23623529411765
Minimum	1
Maximum	243
Zeros	0
Zeros (%)	0.0%
Memory size	33.3 KiB

Quantile statistics

Minimum	1
5-th percentile	35.45
Q1	73
median	100
Q3	127
95-th percentile	167
Maximum	243
Range	242
Interquartile range (IQR)	54

Descriptive statistics

Standard deviation	39.69840057
Coefficient of variation (CV)	0.3960483996
Kurtosis	-0.1321747749
Mean	100.2362353
Median Absolute Deviation (MAD)	27
Skewness	0.1223273244
Sum	426004
Variance	1575.963008

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
90	53	1.2%
87	51	1.2%
93	50	1.2%
100	48	1.1%
120	48	1.1%
105	48	1.1%
116	47	1.1%
98	47	1.1%
127	47	1.1%
112	46	1.1%
Other values (205)	3765	88.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	7	0.2%
2	2	< 0.1%
3	7	0.2%
4	2	< 0.1%
5	2	< 0.1%

Value	Count	Frequency (%)
243	1	< 0.1%
232	2	< 0.1%
225	2	< 0.1%
224	2	< 0.1%
222	2	< 0.1%

area_code
Categorical

Distinct count	3
Unique (%)	0.1%
Missing	0
Missing (%)	0.0%
Memory size	33.3 KiB

area_code_415	2108
area_code_408	1086
area_code_510	1056

Value	Count	Frequency (%)
area_code_415	2108	49.6%
area_code_408	1086	25.6%
area_code_510	1056	24.8%

Length

Max length	13
Mean length	13
Min length	13

Value	Count	Frequency (%)
Lowercase_Letter	6	50.0%
Decimal_Number	5	41.7%
Connector_Punctuation	1	8.3%

Value	Count	Frequency (%)
Latin	6	50.0%
Common	6	50.0%

Value	Count	Frequency (%)
ASCII	12	100.0%

international_plan
Boolean

Distinct count	2
Unique (%)	< 0.1%
Missing	0
Missing (%)	0.0%
Memory size	33.3 KiB

no	3854
yes	396

Frequency Table

Value	Count	Frequency (%)
no	3854	90.7%
yes	396	9.3%

voice_mail_plan
Boolean

Distinct count	2
Unique (%)	< 0.1%
Missing	0
Missing (%)	0.0%
Memory size	33.3 KiB

no	3138
yes	1112

Frequency Table

Value	Count	Frequency (%)
no	3138	73.8%
yes	1112	26.2%

number_vmail_messages
Real number (ℝ_≥0)

ZEROS

Distinct count	46
Unique (%)	1.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	7.631764705882353
Minimum	0
Maximum	52
Zeros	3139
Zeros (%)	73.9%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	0
median	0
Q3	16
95-th percentile	36
Maximum	52
Range	52
Interquartile range (IQR)	16

Descriptive statistics

Standard deviation	13.4398822
Coefficient of variation (CV)	1.761045147
Kurtosis	0.2730383375
Mean	7.631764706
Median Absolute Deviation (MAD)	0
Skewness	1.373091038
Sum	32435
Variance	180.6304335

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
0	3139	73.9%
31	69	1.6%
28	58	1.4%
29	57	1.3%
24	57	1.3%
33	55	1.3%
27	54	1.3%
26	53	1.2%
32	47	1.1%
30	47	1.1%
Other values (36)	614	14.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	3139	73.9%
4	1	< 0.1%
6	2	< 0.1%
8	2	< 0.1%
10	4	0.1%

Value	Count	Frequency (%)
52	1	< 0.1%
50	2	< 0.1%
49	3	0.1%
48	4	0.1%
47	4	0.1%

total_day_minutes
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	1843
Unique (%)	43.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	180.2596
Minimum	0.0
Maximum	351.5
Zeros	2
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	91.59
Q1	143.325
median	180.45
Q3	216.2
95-th percentile	271.055
Maximum	351.5
Range	351.5
Interquartile range (IQR)	72.875

Descriptive statistics

Standard deviation	54.01237333
Coefficient of variation (CV)	0.2996365982
Kurtosis	-0.05670971637
Mean	180.2596
Median Absolute Deviation (MAD)	36.6
Skewness	-0.006910229801
Sum	766103.3
Variance	2917.336473

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
189.3	10	0.2%
180	9	0.2%
184.5	8	0.2%
154	8	0.2%
177.1	8	0.2%
168.6	7	0.2%
230.7	7	0.2%
183.6	7	0.2%
197	7	0.2%
185	7	0.2%
Other values (1833)	4172	98.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	2	< 0.1%
2.6	1	< 0.1%
6.6	1	< 0.1%
7.2	1	< 0.1%
7.8	1	< 0.1%

Value	Count	Frequency (%)
351.5	1	< 0.1%
346.8	1	< 0.1%
345.3	1	< 0.1%
338.4	1	< 0.1%
337.4	1	< 0.1%

total_day_calls
Real number (ℝ_≥0)

Distinct count	120
Unique (%)	2.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	99.90729411764706
Minimum	0
Maximum	165
Zeros	2
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	67
Q1	87
median	100
Q3	113
95-th percentile	133
Maximum	165
Range	165
Interquartile range (IQR)	26

Descriptive statistics

Standard deviation	19.85081731
Coefficient of variation (CV)	0.1986923726
Kurtosis	0.1935936484
Mean	99.90729412
Median Absolute Deviation (MAD)	13
Skewness	-0.08581246337
Sum	424606
Variance	394.054948

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
105	101	2.4%
95	97	2.3%
110	92	2.2%
94	92	2.2%
112	90	2.1%
102	89	2.1%
97	88	2.1%
107	87	2.0%
100	85	2.0%
108	84	2.0%
Other values (110)	3345	78.7%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	2	< 0.1%
30	1	< 0.1%
34	1	< 0.1%
35	1	< 0.1%
36	1	< 0.1%

Value	Count	Frequency (%)
165	1	< 0.1%
160	2	< 0.1%
158	2	< 0.1%
157	2	< 0.1%
156	3	0.1%

total_day_charge
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	1843
Unique (%)	43.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	30.644682352941174
Minimum	0.0
Maximum	59.76
Zeros	2
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	15.5735
Q1	24.365
median	30.68
Q3	36.75
95-th percentile	46.081
Maximum	59.76
Range	59.76
Interquartile range (IQR)	12.385

Descriptive statistics

Standard deviation	9.182096033
Coefficient of variation (CV)	0.2996309744
Kurtosis	-0.0565844345
Mean	30.64468235
Median Absolute Deviation (MAD)	6.225
Skewness	-0.006912526228
Sum	130239.9
Variance	84.31088755

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
32.18	10	0.2%
30.6	9	0.2%
30.11	8	0.2%
31.37	8	0.2%
26.18	8	0.2%
31.45	7	0.2%
34.58	7	0.2%
29.58	7	0.2%
28.63	7	0.2%
28.66	7	0.2%
Other values (1833)	4172	98.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	2	< 0.1%
0.44	1	< 0.1%
1.12	1	< 0.1%
1.22	1	< 0.1%
1.33	1	< 0.1%

Value	Count	Frequency (%)
59.76	1	< 0.1%
58.96	1	< 0.1%
58.7	1	< 0.1%
57.53	1	< 0.1%
57.36	1	< 0.1%

total_eve_minutes
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	1773
Unique (%)	41.7%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	200.17390588235293
Minimum	0.0
Maximum	359.3
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	118.2
Q1	165.925
median	200.7
Q3	233.775
95-th percentile	282.71
Maximum	359.3
Range	359.3
Interquartile range (IQR)	67.85

Descriptive statistics

Standard deviation	50.24951818
Coefficient of variation (CV)	0.2510293135
Kurtosis	0.04345320215
Mean	200.1739059
Median Absolute Deviation (MAD)	33.7
Skewness	-0.03041458624
Sum	850739.1
Variance	2525.014078

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
230.9	10	0.2%
187.5	9	0.2%
194	9	0.2%
169.9	9	0.2%
199.7	9	0.2%
201	8	0.2%
216.5	8	0.2%
223.5	8	0.2%
209.4	8	0.2%
211.5	8	0.2%
Other values (1763)	4164	98.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
22.3	1	< 0.1%
37.8	1	< 0.1%
41.7	1	< 0.1%
42.2	1	< 0.1%

Value	Count	Frequency (%)
359.3	1	< 0.1%
352.1	1	< 0.1%
351.6	1	< 0.1%
349.4	1	< 0.1%
348.5	1	< 0.1%

total_eve_calls
Real number (ℝ_≥0)

Distinct count	123
Unique (%)	2.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	100.17647058823529
Minimum	0
Maximum	170
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	67
Q1	87
median	100
Q3	114
95-th percentile	133
Maximum	170
Range	170
Interquartile range (IQR)	27

Descriptive statistics

Standard deviation	19.9085911
Coefficient of variation (CV)	0.1987352019
Kurtosis	0.1145997215
Mean	100.1764706
Median Absolute Deviation (MAD)	13
Skewness	-0.02081182363
Sum	425750
Variance	396.3519998

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
105	98	2.3%
103	96	2.3%
91	95	2.2%
97	91	2.1%
94	88	2.1%
96	88	2.1%
108	88	2.1%
88	87	2.0%
101	86	2.0%
104	85	2.0%
Other values (113)	3348	78.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
12	1	< 0.1%
36	1	< 0.1%
38	1	< 0.1%
43	1	< 0.1%

Value	Count	Frequency (%)
170	1	< 0.1%
169	1	< 0.1%
168	1	< 0.1%
159	1	< 0.1%
157	1	< 0.1%

total_eve_charge
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	1572
Unique (%)	37.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	17.015011764705886
Minimum	0.0
Maximum	30.54
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	10.05
Q1	14.1025
median	17.06
Q3	19.8675
95-th percentile	24.031
Maximum	30.54
Range	30.54
Interquartile range (IQR)	5.765

Descriptive statistics

Standard deviation	4.271211992
Coefficient of variation (CV)	0.2510260969
Kurtosis	0.04332949445
Mean	17.01501176
Median Absolute Deviation (MAD)	2.86
Skewness	-0.03038789084
Sum	72313.8
Variance	18.24325188

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
16.12	13	0.3%
18.79	13	0.3%
14.25	13	0.3%
16.97	12	0.3%
15.9	12	0.3%
18.96	11	0.3%
16.8	10	0.2%
19.63	10	0.2%
17.09	10	0.2%
16.41	9	0.2%
Other values (1562)	4137	97.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
1.9	1	< 0.1%
3.21	1	< 0.1%
3.54	1	< 0.1%
3.59	1	< 0.1%

Value	Count	Frequency (%)
30.54	1	< 0.1%
29.93	1	< 0.1%
29.89	1	< 0.1%
29.7	1	< 0.1%
29.62	1	< 0.1%

total_night_minutes
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	1757
Unique (%)	41.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	200.52788235294116
Minimum	0.0
Maximum	395.0
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	118.09
Q1	167.225
median	200.45
Q3	234.7
95-th percentile	282.71
Maximum	395
Range	395
Interquartile range (IQR)	67.475

Descriptive statistics

Standard deviation	50.35354807
Coefficient of variation (CV)	0.251104971
Kurtosis	0.1148535776
Mean	200.5278824
Median Absolute Deviation (MAD)	33.55
Skewness	0.008490819348
Sum	852243.5
Variance	2535.479804

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
186.2	11	0.3%
208.9	10	0.2%
188.2	8	0.2%
169.4	8	0.2%
193.6	8	0.2%
230.1	8	0.2%
190.5	8	0.2%
228.1	8	0.2%
214.7	8	0.2%
214	8	0.2%
Other values (1747)	4165	98.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
23.2	1	< 0.1%
43.7	1	< 0.1%
45	1	< 0.1%
46.7	1	< 0.1%

Value	Count	Frequency (%)
395	1	< 0.1%
381.9	1	< 0.1%
381.6	1	< 0.1%
377.5	1	< 0.1%
367.7	1	< 0.1%

total_night_calls
Real number (ℝ_≥0)

Distinct count	128
Unique (%)	3.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	99.8395294117647
Minimum	0
Maximum	175
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	67
Q1	86
median	100
Q3	113
95-th percentile	132
Maximum	175
Range	175
Interquartile range (IQR)	27

Descriptive statistics

Standard deviation	20.09321979
Coefficient of variation (CV)	0.2012551532
Kurtosis	0.07721835856
Mean	99.83952941
Median Absolute Deviation (MAD)	14
Skewness	0.005273110227
Sum	424318
Variance	403.7374815

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
105	100	2.4%
99	92	2.2%
95	91	2.1%
102	90	2.1%
91	88	2.1%
94	88	2.1%
104	87	2.0%
98	87	2.0%
100	86	2.0%
109	85	2.0%
Other values (118)	3356	79.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
33	1	< 0.1%
36	1	< 0.1%
38	2	< 0.1%
40	1	< 0.1%

Value	Count	Frequency (%)
175	1	< 0.1%
170	1	< 0.1%
165	1	< 0.1%
164	1	< 0.1%
161	1	< 0.1%

total_night_charge
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	992
Unique (%)	23.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	9.023891764705883
Minimum	0.0
Maximum	17.77
Zeros	1
Zeros (%)	< 0.1%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	5.3145
Q1	7.5225
median	9.02
Q3	10.56
95-th percentile	12.7255
Maximum	17.77
Range	17.77
Interquartile range (IQR)	3.0375

Descriptive statistics

Standard deviation	2.265921811
Coefficient of variation (CV)	0.2511025033
Kurtosis	0.1148651735
Mean	9.023891765
Median Absolute Deviation (MAD)	1.51
Skewness	0.008444754041
Sum	38351.54
Variance	5.134401655

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
9.4	18	0.4%
9.63	17	0.4%
8.15	17	0.4%
10.8	17	0.4%
9.66	16	0.4%
8.82	15	0.4%
10.49	15	0.4%
9.76	15	0.4%
8.57	14	0.3%
10.35	14	0.3%
Other values (982)	4092	96.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
1.04	1	< 0.1%
1.97	1	< 0.1%
2.03	1	< 0.1%
2.1	1	< 0.1%

Value	Count	Frequency (%)
17.77	1	< 0.1%
17.19	1	< 0.1%
17.17	1	< 0.1%
16.99	1	< 0.1%
16.55	1	< 0.1%

total_intl_minutes
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	168
Unique (%)	4.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	10.256070588235294
Minimum	0.0
Maximum	20.0
Zeros	22
Zeros (%)	0.5%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	5.7
Q1	8.5
median	10.3
Q3	12
95-th percentile	14.6
Maximum	20
Range	20
Interquartile range (IQR)	3.5

Descriptive statistics

Standard deviation	2.760101726
Coefficient of variation (CV)	0.2691188309
Kurtosis	0.7029511928
Mean	10.25607059
Median Absolute Deviation (MAD)	1.8
Skewness	-0.2413595394
Sum	43588.3
Variance	7.618161539

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
11.1	75	1.8%
9.8	73	1.7%
11.4	73	1.7%
10.2	72	1.7%
10.9	71	1.7%
11.3	70	1.6%
10.1	69	1.6%
9.7	68	1.6%
9.5	66	1.6%
10.5	66	1.6%
Other values (158)	3547	83.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	22	0.5%
0.4	1	< 0.1%
1.1	2	< 0.1%
1.3	1	< 0.1%
2	2	< 0.1%

Value	Count	Frequency (%)
20	1	< 0.1%
19.7	2	< 0.1%
19.3	1	< 0.1%
19.2	1	< 0.1%
18.9	1	< 0.1%

total_intl_calls
Real number (ℝ_≥0)

Distinct count	21
Unique (%)	0.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	4.426352941176471
Minimum	0
Maximum	20
Zeros	22
Zeros (%)	0.5%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	1
Q1	3
median	4
Q3	6
95-th percentile	9
Maximum	20
Range	20
Interquartile range (IQR)	3

Descriptive statistics

Standard deviation	2.463069113
Coefficient of variation (CV)	0.5564556522
Kurtosis	3.263227525
Mean	4.426352941
Median Absolute Deviation (MAD)	1
Skewness	1.360122209
Sum	18812
Variance	6.066709454

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
3	847	19.9%
4	795	18.7%
2	644	15.2%
5	598	14.1%
6	408	9.6%
7	272	6.4%
1	226	5.3%
8	153	3.6%
9	126	3.0%
10	59	1.4%
Other values (11)	122	2.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	22	0.5%
1	226	5.3%
2	644	15.2%
3	847	19.9%
4	795	18.7%

Value	Count	Frequency (%)
20	1	< 0.1%
19	1	< 0.1%
18	4	0.1%
17	1	< 0.1%
16	7	0.2%

total_intl_charge
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct count	168
Unique (%)	4.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	2.7696541176470584
Minimum	0.0
Maximum	5.4
Zeros	22
Zeros (%)	0.5%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	1.54
Q1	2.3
median	2.78
Q3	3.24
95-th percentile	3.94
Maximum	5.4
Range	5.4
Interquartile range (IQR)	0.94

Descriptive statistics

Standard deviation	0.7452041364
Coefficient of variation (CV)	0.2690603609
Kurtosis	0.7033212689
Mean	2.769654118
Median Absolute Deviation (MAD)	0.48
Skewness	-0.2416706661
Sum	11771.03
Variance	0.5553292049

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
3	75	1.8%
3.08	73	1.7%
2.65	73	1.7%
2.75	72	1.7%
2.94	71	1.7%
3.05	70	1.6%
2.73	69	1.6%
2.62	68	1.6%
2.84	66	1.6%
2.57	66	1.6%
Other values (158)	3547	83.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	22	0.5%
0.11	1	< 0.1%
0.3	2	< 0.1%
0.35	1	< 0.1%
0.54	2	< 0.1%

Value	Count	Frequency (%)
5.4	1	< 0.1%
5.32	2	< 0.1%
5.21	1	< 0.1%
5.18	1	< 0.1%
5.1	1	< 0.1%

number_customer_service_calls
Real number (ℝ_≥0)

ZEROS

Distinct count	10
Unique (%)	0.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	1.5590588235294118
Minimum	0
Maximum	9
Zeros	886
Zeros (%)	20.8%
Memory size	33.3 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	1
median	1
Q3	2
95-th percentile	4
Maximum	9
Range	9
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	1.31143353
Coefficient of variation (CV)	0.8411700126
Kurtosis	1.655618759
Mean	1.559058824
Median Absolute Deviation (MAD)	1
Skewness	1.082691586
Sum	6626
Variance	1.719857904

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	1524	35.9%
2	947	22.3%
0	886	20.8%
3	558	13.1%
4	209	4.9%
5	81	1.9%
6	28	0.7%
7	13	0.3%
9	2	< 0.1%
8	2	< 0.1%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	886	20.8%
1	1524	35.9%
2	947	22.3%
3	558	13.1%
4	209	4.9%

Value	Count	Frequency (%)
9	2	< 0.1%
8	2	< 0.1%
7	13	0.3%
6	28	0.7%
5	81	1.9%

churn
Boolean

Distinct count	2
Unique (%)	< 0.1%
Missing	0
Missing (%)	0.0%
Memory size	33.3 KiB

no	3652
yes	598

Frequency Table

Value	Count	Frequency (%)
no	3652	85.9%
yes	598	14.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Cramér's V (φc)

Cramér's V is an association measure for nominal random variables. The coefficient ranges from 0 to 1, with 0 indicating independence and 1 indicating perfect association. The empirical estimators used for Cramér's V have been proved to be biased, even for large samples. We use a bias-corrected measure that has been proposed by Bergsma in 2013 that can be found here.

Count
Matrix

First rows

	state	account_length	area_code	international_plan	voice_mail_plan	number_vmail_messages	total_day_minutes	total_day_calls	total_day_charge	total_eve_minutes	total_eve_calls	total_eve_charge	total_night_minutes	total_night_calls	total_night_charge	total_intl_minutes	total_intl_calls	total_intl_charge	number_customer_service_calls	churn
0	OH	107	area_code_415	no	yes	26	161.6	123	27.47	195.5	103	16.62	254.4	103	11.45	13.7	3	3.70	1	no
1	NJ	137	area_code_415	no	no	0	243.4	114	41.38	121.2	110	10.30	162.6	104	7.32	12.2	5	3.29	0	no
2	OH	84	area_code_408	yes	no	0	299.4	71	50.90	61.9	88	5.26	196.9	89	8.86	6.6	7	1.78	2	no
3	OK	75	area_code_415	yes	no	0	166.7	113	28.34	148.3	122	12.61	186.9	121	8.41	10.1	3	2.73	3	no
4	MA	121	area_code_510	no	yes	24	218.2	88	37.09	348.5	108	29.62	212.6	118	9.57	7.5	7	2.03	3	no
5	MO	147	area_code_415	yes	no	0	157.0	79	26.69	103.1	94	8.76	211.8	96	9.53	7.1	6	1.92	0	no
6	LA	117	area_code_408	no	no	0	184.5	97	31.37	351.6	80	29.89	215.8	90	9.71	8.7	4	2.35	1	no
7	WV	141	area_code_415	yes	yes	37	258.6	84	43.96	222.0	111	18.87	326.4	97	14.69	11.2	5	3.02	0	no
8	IN	65	area_code_415	no	no	0	129.1	137	21.95	228.5	83	19.42	208.8	111	9.40	12.7	6	3.43	4	yes
9	RI	74	area_code_415	no	no	0	187.7	127	31.91	163.4	148	13.89	196.0	94	8.82	9.1	5	2.46	0	no

Last rows

	state	account_length	area_code	international_plan	voice_mail_plan	number_vmail_messages	total_day_minutes	total_day_calls	total_day_charge	total_eve_minutes	total_eve_calls	total_eve_charge	total_night_minutes	total_night_calls	total_night_charge	total_intl_minutes	total_intl_calls	total_intl_charge	number_customer_service_calls	churn
4240	AR	127	area_code_415	no	yes	27	157.6	107	26.79	280.6	49	23.85	75.1	77	3.38	8.0	4	2.16	1	no
4241	WA	80	area_code_510	no	no	0	157.0	101	26.69	208.8	127	17.75	113.3	109	5.10	16.2	2	4.37	2	no
4242	MN	150	area_code_408	no	no	0	170.0	115	28.90	162.7	138	13.83	267.2	77	12.02	8.3	2	2.24	0	no
4243	ND	140	area_code_510	no	no	0	244.7	115	41.60	258.6	101	21.98	231.3	112	10.41	7.5	6	2.03	1	yes
4244	AZ	97	area_code_510	no	no	0	252.6	89	42.94	340.3	91	28.93	256.5	67	11.54	8.8	5	2.38	1	yes
4245	MT	83	area_code_415	no	no	0	188.3	70	32.01	243.8	88	20.72	213.7	79	9.62	10.3	6	2.78	0	no
4246	WV	73	area_code_408	no	no	0	177.9	89	30.24	131.2	82	11.15	186.2	89	8.38	11.5	6	3.11	3	no
4247	NC	75	area_code_408	no	no	0	170.7	101	29.02	193.1	126	16.41	129.1	104	5.81	6.9	7	1.86	1	no
4248	HI	50	area_code_408	no	yes	40	235.7	127	40.07	223.0	126	18.96	297.5	116	13.39	9.9	5	2.67	2	no
4249	VT	86	area_code_415	no	yes	34	129.4	102	22.00	267.1	104	22.70	154.8	100	6.97	9.3	16	2.51	0	no

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Cramér's V (φc)

Missing values

Sample

First rows

Last rows